Systems of linear forms and covers for star bodies

M. M. Dodson

Acta Arithmetica (1992)

  • Volume: 61, Issue: 2, page 119-127
  • ISSN: 0065-1036

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M. M. Dodson. "Systems of linear forms and covers for star bodies." Acta Arithmetica 61.2 (1992): 119-127. <http://eudml.org/doc/206455>.

@article{M1992,
author = {M. M. Dodson},
journal = {Acta Arithmetica},
keywords = {metric diophantine approximation; systems of linear forms; cover; star body; Hausdorff dimension},
language = {eng},
number = {2},
pages = {119-127},
title = {Systems of linear forms and covers for star bodies},
url = {http://eudml.org/doc/206455},
volume = {61},
year = {1992},
}

TY - JOUR
AU - M. M. Dodson
TI - Systems of linear forms and covers for star bodies
JO - Acta Arithmetica
PY - 1992
VL - 61
IS - 2
SP - 119
EP - 127
LA - eng
KW - metric diophantine approximation; systems of linear forms; cover; star body; Hausdorff dimension
UR - http://eudml.org/doc/206455
ER -

References

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  1. [1] J. D. Bovey and M. M. Dodson, The fractional dimension of sets whose simultaneous rational approximations have errors with a small product, Bull. London Math. Soc. 10 (1978), 213-218. Zbl0384.10013
  2. [2] J. D. Bovey and M. M. Dodson, The Hausdorff dimension of systems of linear forms, Acta Arith. 45 (1986), 337-358. Zbl0534.10025
  3. [3] J. W. S. Cassels, An Introduction to the Geometry of Numbers, Grundlehren Math. Wiss. 99, Springer, Berlin 1959. 
  4. [4] M. M. Dodson, A note on the Hausdorff-Besicovitch dimension of systems of linear forms, Acta Arith. 44 (1985), 87-98. 
  5. [5] M. M. Dodson, Star bodies and Diophantine approximation, J. London Math. Soc. 44 (1991), 1-8. 
  6. [6] H. G. Eggleston, Sets of fractional dimensions which occur in some problems of number theory, Proc. London Math. Soc. 54 (1951-1952), 42-93. Zbl0045.16603
  7. [7] K. J. Falconer, The Geometry of Fractal Sets, Cambridge Tracts in Math. 85, Cambridge University Press, Cambridge 1985. 
  8. [8] P. Gruber and C. G. Lekkerkerker, Geometry of Numbers, North-Holland, Amsterdam 1987. Zbl0611.10017
  9. [9] W. K. Hayman, Meromorphic Functions, Oxford Math. Monographs, Clarendon Press, Oxford 1964. 
  10. [10] V. Jarník, Über die simultanen diophantischen Approximationen, Math. Z. 33 (1931), 505-543. Zbl57.1370.01
  11. [11] H. Rüssmann, On the one-dimensional Schrödinger equation with a quasi-periodic potential, Ann. New York Acad. Sci. 357 (1980), 90-107. 
  12. [12] V. G. Sprindžuk, Metric Theory of Diophantine Approximations, translated by R. A. Silverman, V. H. Winston & Sons, Washington, D.C., 1979. Zbl0287.10043
  13. [13] K. Yu, Hausdorff dimension and simultaneous rational approximation, J. London Math. Soc. 24 (1981), 79-84 Zbl0427.28008

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